Nanocrystal superlattices with thermally degradable hybrid inorganic-organic capping ligands

Colloidal metallic and semiconductor nanocrystals (NCs) functionalized with metal chalcogenide complexes (MCCs) have shown a promise for designing materials that combine high carrier mobility with the electronic structure of strongly quantum-confined solids. Here we report a simple and general methodology for switching the repulsive forces responsible for colloidal stabilization of MCC-capped NCs from long-range electrostatic to short-range steric through the formation of tight ionic pairs with cationic surfactants. This noncovalent surface modification remarkably improved the ability of MCC-capped NCs to self-assemble into long-range ordered superlattices. These NCs are highly soluble in nonpolar solvents and compatible with various technologically relevant organic molecules and polymers. The hybrid inorganic-organic coating can be thermally decomposed at significantly lower temperatures compared to those required for removal of conventional organic ligands.     

Neutron optics of strongly absorbing media and interaction of long-wave neutrons with gadolinium films

The modern state of neutron optics of absorbing media is briefly surveyed. In all probability, there are no physics arguments that would constrain, in the case of strong absorption, the applicability of the commonly accepted Fermi-Foldy dispersion law for neutron waves. In accord with previously known results, it is found that the coefficient of reflection of neutrons from the boundary of a strongly absorbing medium tends to unity with decreasing velocity of neutrons incident on this medium. At low neutron energies peculiar to the case of ultracold neutrons, the complex scattering length for neutron-nucleus interaction proves to be constant, whence it follows that the cross section for neutron capture by a free nucleus obeys the 1/v law. The cross section for the analogous process on nuclei within a medium is described by the 1/v′ law, where v′=?k′/m, with k′ being the real part of the neutron wave number in the medium. As the incident-neutron velocity v decreases, the velocity v′ in a medium tends to some limiting value. From the coefficient of reflection of cold neutrons that is measured as a function of the wavelength and the angle of incidence, a refined value is found for the real part of the scattering length for neutron interaction with gadolinium nuclei. An experiment was performed where ultracold neutrons were transmitted through thin samples containing natural gadolinium. In analyzing the results of this experiment, use was made of the value found here for the real part of the neutron-nucleus scattering length. The experiment indicates that the imaginary part of the scattering length is a constant or, what is the same, that, for neutron velocities ranging from 4 to about 120 m/s, the 1/v law for the cross section for neutron capture by a free nucleus is valid to within 6%.     

On the Existence of a Noninner Automorphism of Order p for p-Groups

We obtain sufficient conditions for the existence of a noninner automorphism of order p for finite p-groups. We show that groups of order p ⁿ (n < 7, p is a prime number, p > 3) possess a noninner automorphism of order p.     

On the endomorphisms of translation modules of polynomials

We determine the structure of a ring of endomorphisms of a translation module whose structure is determined by a group of translations of an affine space that acts by means of displacement on a polynomial algebra.     

Structural defects in periodic and quasicrystalline binary nanocrystal superlattices

Binary nanocrystal superlattices (BNSLs) emerge as an important class of man-made materials where components and functionalities can be added, tuned, or combined in a predictable manner. These amazingly complex structures spontaneously self-assemble from colloidal solutions containing binary mixtures of functional (semiconducting, magnetic, plasmonic, etc.) nanocrystals. Further developments of the BNSL-based materials require a deep understanding and control over BNSL formation and structural perfection. Like any solid, BNSL can contain different kinds of structural defects. It is well-known that defects can have a tremendous effect on the material's behavior. Defect engineering is used to modify and improve many of the mechanical, electrical, magnetic, and optical properties of conventional solids. In this work, we provide the first systematic analysis of structural defects in various BNSL structures. We used BNSLs as a platform for studying structural defects in both periodic (crystalline) and aperiodic (quasicrystalline) lattices, as well as for direct imaging of the interfaces between crystalline and quasicrystalline domains. Such direct observation of local imperfections in complex multicomponent lattices provides a unique insight into the fundamental aspects of crystal formation.     

Geometric factor in the spin-echo small-angle neutron scattering technique based on magnetic fields that increase linearly with time

The sensitivity of the spin-echo small-angle neutron scattering technique based on magnetic fields that increase linearly with time is analyzed depending on the scattering geometry and the detector apperture. The application of sectoral collimators for the selection of scattering neutron trajectories is substantiated with the aim of improving the resolution and the corresponding effect on the data acquisition time is estimated.     

Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra

We study locally nilpotent derivations belonging to a Lie algebra sa _n of a special affine Cremona group in connection with the root decompositions of sa _n relative to the maximum standard torus. It is proved that all root locally nilpotent derivations are elementary. As a continuation of this research, we describe two- and three-root derivations. By using the results obtained by Shestakov and Umirbaev, it is shown that the exponents of almost all obtained three-root derivations are wild automorphisms of a polynomial algebra in three variables.     

Properties of freely suspended liquid crystal films and their applications

We report the review on the physical properties of the liquid crystal freely suspended films. The importance of the freely suspended films for the study of the fundamental problems of the self-confined systems as well as their practical implementations are demonstrated.     

On the isomorphism of wreath products of groups

The well-known Neumann theorem on the isomorphism of standard wreath products is generalized to the wreath products of an arbitrary transitive permutation group and an abstract group. Pedagogical Institute, Vinnitsa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 671–679, June, 1994